At about 54:20, when Leon is in a straitjacket in a cell, the right hand "stone" wall wobbles quite markedly when he bumps into it.
There appears to be a large personal computer on the doctor's desk. Since the movie is set in the 1960's, such a computer would not have been available for another decade.
The story takes place in 1959, yet in the Stone family's kitchen, there is a box of Quisp cereal, which was first sold in 1965.